Express your answer as a mixed number simplified to lowest terms. $6\dfrac{3}{5}-1\dfrac{3}{4} = {?}$
Solution: Find a common denominator for the fractions: $= {6\dfrac{12}{20}}-{1\dfrac{15}{20}}$ Convert ${6\dfrac{12}{20}}$ to ${5 + \dfrac{20}{20} + \dfrac{12}{20}}$ So the problem becomes: ${5\dfrac{32}{20}}-{1\dfrac{15}{20}}$ Separate the whole numbers from the fractional parts: $= {5} + {\dfrac{32}{20}} - {1} - {\dfrac{15}{20}}$ Bring the whole numbers together and the fractions together: $= {5} - {1} + {\dfrac{32}{20}} - {\dfrac{15}{20}}$ Subtract the whole numbers: $=4 + {\dfrac{32}{20}} - {\dfrac{15}{20}}$ Subtract the fractions: $= 4+\dfrac{17}{20}$ Combine the whole and fractional parts into a mixed number: $= 4\dfrac{17}{20}$